1. Place nuts in a 9-inch pie pan and bake in a 350° regular or convection oven until golden, 5 to 7 minutes.
2. Meanwhile, chop tomatoes. In a small bowl, mix oil and butter.
3. Cut filo sheets into 12-inch squares. One at a time, brush squares lightly with butter mixture and stack.
4. Spread chopped tomatoes, basil, and toasted nuts in center of filo stack in a round that matches the size of the cheese. Place cheese on top of tomato mixture. Fold corners of filo stack, one at a time, over cheese and brush lightly with butter mixture. Press filo against cheese to make a smooth package.
5. Place wrapped cheese, smooth side up, in 9-inch pie pan. Brush top of filo with remaining butter mixture.
6. Bake in a 350° regular or convection oven until filo is golden, 25 to 30 minutes. Cool about 10 minutes.
7. With a wide spatula, transfer filo-wrapped brie to a plate. To serve, cut a big X in center or cut off a corner so guests can scoop out cheese mixture.